Graphical Display of a Physics Simulation

Size: px
Start display at page:

Download "Graphical Display of a Physics Simulation"

Transcription

1 Graphical Display of a Physics Simulation Steven Oetjen TJHSST Computer Systems Lab, March 29, 2007 Abstract A physics simulation, in order to adequately demonstrate physical laws and predict an unlimited number of scenarios, must implement a broad range of mathematical equations and provide the user with the ability to set up a scenario with whatever number of objects and arrangements of these objects that he desires. The goal of this project is to create such a simulation. 1 Introduction The desired physics simulation and graphical display must govern a set of objects under the laws of physics, such as Newton s laws of motion. Accuracy and precision are important when measuring quantities for use in calculations, but it is also important to have a simulation process all objects and apply physical laws efficiently. The program, in other words, must run in real time or at a speed chosen by the user. Such a simulation is worthwhile and valuable because it provides an opportunity to quickly and easily test or verify phenomena, utilizing a computer s ability to store, manipulate, and display data. The results may attract the interest of many, including students needing an aid in their understanding of the physical world and how it behaves. The results can also be used to make or to confirm predictions on how certain scenarios will be resolved. This simulation is intended to display objects placed by the user graphically and to display information about those objects on a graphical user interface. The project will allow the user to place any combination of objects, including particles, springs, and ramps, in a graphical display, input values for these objects, such as constants, coefficients, and variables, and run a simulation that will track these values and display the interactions and positions of the objects graphically in two-dimensions. The scope of the simulation will be limited to two-dimensions with particles, springs, and ramps, thus constricting the field of study. The concepts involved are kinematics, dynamics and Newton s laws, conservation of momentum and collisions, gravitational force, and electric charge and force. Variables such as mass, displacement, velocity, and charge, only to name a few, are required, as well as the relationships between these variables in the form of equations. 1

2 2 Background A similar simulation was written in Java by Erik Neumann, named My Physics Lab [3]. Newmann s program consists of a series of java applets that run various scenarios based on user input for chosen quantities. Rather than having a large interface in which the user can create any scenario imaginable, with all the same laws governing each scenario,there are several pre-set scenarios, each with a set of laws governing it, as other laws might not be applicable. This organization allows Neumann to cover a broad range of objects, including linear springs, pendulums, colliding blocks, roller coasters, and molecules. It also graphs two quantities of the user s choice over time, and provides mathematical equations for all scenarios. A model for pressure on a soft body was created by Matyka [7]. It takes into account gravitational and spring forces, and pressure. It also implements a first order Euler integrater to calulate force accumulations necessary for finding the volume of a body and pressure force distribution. He applies these calculations to a 2D soft ball model and a 3D pressure soft body model. 2.1 Kinematics Two-dimensional kinematics involve the position, velocity, and acceleration vectors of an object [2]. Since velocity is the derivative of position, the linear approximation of x after a small time interval t is, x = x 0 + v t (1) and the linear approximation of v after t is, v = v 0 + a t (2) As t 0, these approximations become more accurate in calculating position and velocity, so a small time interval is necessary. 2.2 Collision Detection and Response A method for improved collision detection applies matrices and vector space to a sweep method over a polygon soup of triangles [6]. A much simpler method to apply to twodimensional circle objects to check for overlap is a simple comparison between the sum of their radii and the distance between their centers. r 1 + r 2 (x 2 x 1 ) 2 + (y 2 y 1 ) 2 (3) When a collision is detected, that is, if condition 3 is true, then for an elastic collision, the velocities of the objects involved must be changed so that both kinetic energy and momentum of the system are conserved [8]. 1 2 m av 2 a m bv 2 b = 1 2 m av 2 a m bv 2 b (4) m a v a + m b v b = m a v a + m b v b (5) 2

3 Solving equations 4 and 5 for v a and v b, v a = m a m b v a + 2m b v b (6) m a + m b m a + m b v b = 2m a v a m a m b v b (7) m a + m b m a + m b the velocities of both objects after the collision are found. These equations can be extended to two dimensions by performing them for both an x- and y-component. Using these methods for collision response, however, does not take into account angular effects of collision. There are vector equations that can account for this [1]. v A 2 = v A 1 + j M A n (8) v2 B = v1 B + j M n (9) B (1 + e)vab 1 n j = n n( (10) ) M A M B By finding the scalar j, based on the elasticity of the two objects and the normal vector of there velocities before the collision, the velocities after the collision can be found. Momentum is still conserved in both components, and the effects of the initial angle of collision will be produced in non-head-on collisions. 2.3 Contact With Ramps and Response In order to determine if a projectile is in contact with a ramp, the ramp can be represented by a linear equation of the form y = mx + b. Using variables b min to represent the y-intercept of the line, b max to represent that intercept plus an additional r proj to cosθ compensate for the radius of the projectile, and an additional t ramp cosθ to compensate for the thickness of the ramp, two conditions must be true for contact between the ramp and projectile. x ramp,1 x proj x ramp,2 (11) mx proj + b min + t ramp cosθ y proj mx proj + b max + t ramp cosθ (12) If a projectile is in contact with a ramp, it exerts a force on it, and so by Newton s third law, that every action force has an equal and opposite reaction force, the ramp must exert an opposite force back. This force is perpendicular to the surface of the ramp. The equations for the force components exerted on a projectile due to the ramp, exerting horizontal force, are F x = F horiz sin 2 θ (13) F y = F horiz cosθsinθ (14) while the equations for the force components exerted on a projectile due to the ramp, exerting vertical force, are F x = F vert sinθcosθ (15) 3

4 F y = F vert cos 2 θ (16) In addition, if conditions 11 and 12 are true, the velocity of the projectile must be changed so that the component parallel to the surface of the ramp is unchanged, and the component perpendicular to the ramp is reversed. v = v (17) v = v (18) The components of the projectile s velocity are found parallel and perpendicular to the ramp, using the equations, v = v x cosθ + v y sinθ (19) v = v x sinθ + v y cosθ (20) If the perpendicular component of the velocity is negative, meaning the projectile is going into the ramp, the velocity of the projectile needs to be changed so that the component parallel to the ramp is unchanged and the perpendicular component is reversed. In order to do this, adjustments are made using the following formulas: v x = v cosθ + v sinθ (21) v y = v sinθ v cosθ (22) By substituting equations 21 and 22 into equation 19, the desired relationship in equation 17 is obtained. v = (v cosθ + v sinθ)cosθ + (v sinθ v cosθ)sinθ v = v (cos 2 θ + sin 2 θ) + v sinθcosθ v cosθsinθ v = v Similarly, by substituting equations 21 and 22 into equation 20, the desired relationship in equation 18 is obtained. 2.4 Spring Force v = (v cosθ + v sinθ)sinθ + (v sinθ v cosθ)cosθ v = v cosθsinθ + v sinθcosθ v (sin 2 θ + cos 2 θ) v = v Springs have a natural length, l natural, the length at which they are at rest or equilibrium, and at which they exert no force. Different springs also have different stiffnesses, and this is reflected in a spring s stiffness constant, k. Springs exert a force on each end according to Hooke s Law, F spring = kx (23) 4

5 where x is the spring s displacement beyond its natural length. The negative sign is present because the force is a restoring force, meaning that it is in the opposite direction as the displacement [9]. Springs are also subject to a damping force, F damping = bv (24) where b is the damping factor and v is the velocity component of the attached object parallel to the force of the spring. Again, a negative sign is present because the damping force acts against the motion of the spring [?]. 2.5 Inverse Square Forces Gravitational force is the force that attracts all bodies of mass towards each other with the force, F grav = G m 1m 2 r 2 (25) where G is the universal gravitational constant (G = ), m 1 and m 2 are the masses of the two objects, and r is the distance between the two objects [4]. Electrostatic force, or Coulomb force, is the force that attracts objects with different charge signs and repels objects with like charge signs. The force behaves according to the equation, F Coulomb = k q 1q 2 r 2 (26) where k is the Coulomb constant (k = ), q 1 and q 2 are the charges of the two objects, and r is the distance between the two objects [5] 3 Development There are several requirements that must be met to ensure success of the simulation. Inputs must be doubles able to be parsed, given by the user through JTextFields, to any given precision, in the range of doubles able to be stored in memory, and given as often as desired by the user between runs of the simulation. Outputs must be displayed as objects in their respective positions and values in JTextFields and JLabels, to an accuracy of a ±1% error, in the range of doubles able to be stored in memory, and given as frequently as the Timer fires. Calculations for all the objects must be completed within the time elapsed during the timer delay in order to keep the simulation time proportional to real time. This proportionality will be created by the time scale factor the user provides to speed up or slow down the simulation as desired. Success for most of the requirements can be observed qualitatively, such as if objects appear with different names and colors, if values are being recorded to a certain decimal place, if objects overlap or collide properly, or if ramps are drawn with the correct slope and thickness. The requirements that demand quantitative testing are the accuracy of the output, and the efficiency of processing time. The output can be compared to theoretical values or examined in terms of a known equation, and the processing time 5

6 can be judged by comparing elapsed simulation times to elapsed real time for different numbers of active objects. The project was developed by dividing functions into several iterations of design, programming, and testing. The tasks of these iterations include implementing each concept and set of equations and laws. These groups are kinematics, dynamics, momentum, gravitation, and electrostatics. Each iteration proceeded with the following steps: Design Classes, methods, and variables were added or modified, and the function of each element and the means of communication of information between relevant classes was determined. Programming The necessary changes to the program were made. All programming was done in Java, using Swing and AWT packages for graphics and GUI components. Testing To test a given implementation of a law, the user will input arbitrary values for all necessary fields involved in or dependent on that law. The output generated by these random types of input will be compared to theoretical values derived from mathematical formulas. To analyze the error, a percent error calculation will be performed on these two values, and the accuracy will be gauged by that percent. In this way, the accuracy of the program s ability to model predictable phenomena can be measured and displayed in chart format. Aside from implementing equations and laws, several other components to the program must be implemented. 1. GUI Structure and Layout 2. Graphics Panel Distance and Time Scale 3. Support of Multiple Objects/Multiple Types and Classes of Objects 4. Support of Coordinate and Polar Vector Conversions 5. Collision Detection 6. Improved Integration Methods The major classes involved are the GraphicsPanel, which displays the graphical output, and the GUIPanel, which displays the numerical output and reads in the user s input. Other critical classes include Projectiles and Ramps, the objects themselves which store their own quantities, and ProjectileInputs and RampInputs, which provide a GUI layout for input to each object. The architecture is designed so that changes in the future can be easily accomodated. The program is modularized so that new features can be added in without interfering with existing ones. For example, additional types of objects can be created by creating a class for the object and a class for its inputs. Room on the GUI can be allocated for that input, and functions can be added to draw and implement appropriate laws for those objects. 6

7 4 Results and Conclusion To be a successful and useful simulation, the program must implement all equations and relationships correctly, and process all data efficiently. Specific requirements must exist for processing time, kinematics, collisions, ramp forces, and ramp collisions. 4.1 Processing Time No matter how great the number of objects, the program s calculations must not take longer than the timer s firing delay, so that the program runs proportionally to real time. For the processing time analysis, the simulation was run for 10 seconds for each number of objects, n obj, and the real and simulation times elapsed were recorded, as well as a percent error calculation. Processing Time Analysis n obj t sim t real % error The program s processing time successfully meets the requirement, because there is no upward trend in simulation time when the number of objects is increased, so it is not being slowed down by multiple objects, and it is running proportionally to real time. The percent errors appear large because of the human error involved in starting and stopping both a stopwatch and the simulation. The times are consistent, and the percent errors stay relatively constant. 4.2 Kinematics Using any given inputs, a projectile s position at any time later should be accurate to its theoretically predicted position within ±1%. To test the program s accuracy with kinematics in cartesian coordinates, the program was given the following inputs, and the outputs for x were recorded at various times. These values are compared with theoretical values, and a percent error calculation is shown. Value Accuracy for Cartesian Coordinates Inputs x 0 (m) v x0 (m/s) a x0 (m/s 2 ) Outputs 7

8 t(s) x sim x theor % error Note: theoretical values were calculated using the equation for constant acceleration, x = x 0 + v x0 t + 1a 2 x0t 2. The accuracy of the values for cartesian coordinates meets the requirement, because for all of the checked points in time, the simulation s value was within ±1% of the theoretical value. To test the program s accuracy with kinematics in polar coordinates, the program was given the following inputs, and the outputs for x were recorded at various times. These values are compared with theoretical values, and a percent error calculation is shown. Value Accuracy for Polar Coordinates Inputs r (m) θ r ( ) v (m/s) θ v ( ) a (m/s 2 ) θ a ( ) Outputs t(s) r sim r theor % error The error of the values stayed relatively constant, but did reach above a 1% error. This could be because during previous tests, only one dimension was tested, but for this test, both dimensions were necessary because of the nature of polar coordinates. Error could have multiplied with two dimensions. Accuracy in two dimensions is not as high as desired, so a better method of integration is needed to increase the level of accuarcy. 8

9 4.3 Collisions For any collision between two objects, the momentum of the system before the collision must be equal to the momentum after the collision, and for elastic collisions, the same is true of kinetic energy. To test this function, two objects with different masses and velocities were collided, and the initial and final momentums and kinetic energy values were calculated. Two Objects Before and After Collision Object v x, v y p x, p y KE v x, v y p x, p y KE A B Σp x 20.0 Σp x 20.0 Σp y 0.0 Σp y 0.0 ΣKE ΣKE Momemtum was conserved in both the x- and y-components, and kinetic energy was conserved as a scalar. The objects bounced off each other with the appropriate angle, meaning that angular effects of a collision were correctly produced. 4.4 Ramp Forces When a projectile is exerting a force on a ramp, the ramp must exert an equal and opposite force on the projectile. With gravity acting on the projectile, it should slide down the ramp, accelerating parallel to the ramp s surface. A range of angles, both positively and negatively sloped, will be tested to ensure projectiles accelerate parallel to the surface in all cases. The angles to be tested will be -60, -45, -30, 0, 30, 45, and 60, all measured from the positive x-axis. Acceleration Direction of Projectile Sliding Down Various Ramps θ ramp θ acceleration The projectile always is accelerated by the ramp in the same direction the ramp slopes in. Therefore, this test verifies that for any slope of the ramp, a projectile will accelerate in that same direction. 9

10 4.5 Ramp Collisions When a projectile has a velocity component perpendicular and into the surface of a ramp, and they collide, the angle of incidence must equal the angle of reflection after the projectile bounces off. A range of angles, both positively and negatively sloped, will be tested to ensure projectiles bounce off of ramps correctly. The angles to be tested will be -60, -45, -30, 0, 30, 45, and 60, all measured from the positive x-axis. For each velocity adjustment test, the projectile had the same initial velocity of 10 m/s, directed at -90 clockwise from the positive x-axis, and the angle of the ramp varied. Angles of Incidence and Reflection of Projectile Reflected Off Various Ramps θ ramp θ v θ i θ r The angle of incidence is always equal to the angle of reflection, no matter what the angle of the ramp is. Therefore, this test verifies that for any slope of the ramp, a projectile will bounce off of correctly, as v = v and v = v. 4.6 Springs Spring force was tested by recording the position and acceleration of an object attached to a spring for 20 seconds with three different damping factors, b = 0, b = 0.25, and b = 0.5. Initial values of Objects projectile x 15.0 y 0.0 v 0.0 a 0.0 spring k 1.0 l natural 10.0 (x 1, y 1 ) (0, 0) (x 2, y 2 ) [projectile] Position and Acceleration of Object on Spring, b = 0 When the spring has a damping force of 0, the projectile moves along a sinusoidal path centered at its natural length, 10. The acceleration curve behaves like the second derivative of the position curve, as it is 0 at the inflection points of position, that is, 10

11 when the spring is at its natural length. The acceleration, and therefore force (because the mass is 1.0 kg) behaves properly, because it always carries the opposite sign of the difference between the natural length and current position, and both curves have the same amplitude (because the spring constant k = 0). The projectile s peak position, however, increases over time. The maximum position was , which is an error of 5.7% from the original position of 15. The propogation of error in the calculations of position is resulting in a creation of energy over time. Position and Acceleration of Object on Spring, b = 0.25 When the damping factor is increased to 0.25, the position continues to center around the spring s natural length of 10, but the amplitude decreases over time. The acceleration is still behaving as the second derivative of the position. It moves in the opposite manner of the position curve. Position and Acceleration of Object on Spring, b = 0.5 When the damping factor is increased to 0.5, the position curve approaches the natural length of 10 very rapidly, barely performing two cycles before it is oscillating between 9.5 and The acceleration continues to be a reflection of the position curve, showing 11

12 that the force behaves correctly in accelerating the object towards the natural length. 4.7 Inverse Square Forces Gravitational force was tested by recording the position and acceleration of an object with small mass as it is affected by the gravity of a massive object for 20 seconds. Initial values of Objects, Gravitation Test Small Object m 1.0 r 1.0 q 0.0 x 0.0 y 0.0 v 0.0 a 0.0 Large Object m r 5.0 q 0.0 x 20.0 y 0.0 v 0.0 a 0.0 Position and Acceleration of Small Object Affected by Gravity For the gravitation test, the position curve shows the repeated collision with the large body at position x = 20, and the decreasing maximum height of each bounce. The acceleration begins at a certain value, based on the initial distance of 20 m. It increases as the small projectile gets closer to the large one, and there is a discontinuity where the collision occurs. Here, the acceleration begins decreasing as the objects move apart. 12

13 Coulomb force was tested by recording the position and acceleration of two objects with opposite charges for 20 seconds. Initial values of Objects, Electrostatics Test Positive Object m 1.0 r 5.0 q x -20 y 0 v 0.0 a 0.0 Negative Object m 1.0 r 5.0 q x 20.0 y 0.0 v 0.0 a 0.0 Position and Acceleration of Objects of Opposite Charge For the electrostatics test, the two objects positions mirror each other, as they continually bounce off each other. They always have opposite coordinates, and their maximum height decreases with each bounce. Similarly to the gravitation test, the acceleration curves peak in magnitude at the time of the collision. They increase as the objects approach each other and decrease after the collision, after they move apart, until the maximum distance is reached. The acceleration curves then continuously reach a minimum, resulting in a slope of zero for the position curve. The forces are caluclated correctly, and the motion resulting from the forces appears correct. 13

14 4.8 Conclusion The simulation is successful in most areas, and is certainly useful for predicting physical phenomena and aiding students in their understanding of physics. All calculations are performed within the timer delay, so there is no lag when the simulation is run, and all formulas for effects of collision have been verified by testing. Kinematics in one dimension are calculated within ±1%, but the major flaw is that when expanded to two dimensions, the calculations can occasionally rise slightly beyond the desired ±1% error. To fix this, a more accurate method of integration is needed to counteract error that propogates from linear approximations. References [1] C. Hecker, Physics Part 3: Collision Response, Definition Six, Inc. [2] D. C. Giancoli, Physics: Principles with Applications, Prentice Hall, giancoli physicsppa 6/0,8713, ,00.html (November 2, 2006) [3] E. Neumann, My Physics Lab - Physics Simulation with Java, (November 2, 2006) [4] E. W. Weisstein, Gravitational Force, Wolfram Research, [5] E. W. Weisstein, Coulomb s Law, Wolfram Research, [6] K. Fauerby, Improved Collision Detection and Response, (December 11, 2006) 14

15 [7] M. Matyka, How To Implement a Pressure Soft Body Model, maq/soft2d/howtosoftbody.pdf (November 2, 2006) [8] R. Fitzpatrick, Collisions in 1-dimension, (November 30, 2006) [9] R. Vawter, Hooke s Law - Spring Force, Western Washington University, Department of Physics and Astronomy, vawter/physicsnet/topics/shm/hookeslaw.html 15

Chapter 13. Simple Harmonic Motion

Chapter 13. Simple Harmonic Motion Chapter 13 Simple Harmonic Motion Hooke s Law F s = - k x F s is the spring force k is the spring constant It is a measure of the stiffness of the spring A large k indicates a stiff spring and a small

More information

Chapter 15 Periodic Motion

Chapter 15 Periodic Motion Chapter 15 Periodic Motion Slide 1-1 Chapter 15 Periodic Motion Concepts Slide 1-2 Section 15.1: Periodic motion and energy Section Goals You will learn to Define the concepts of periodic motion, vibration,

More information

Physics I. Unit 1 Methods in Science (Systems of Units) Competencies (Do) Students should be able to demonstrate scientific methods.

Physics I. Unit 1 Methods in Science (Systems of Units) Competencies (Do) Students should be able to demonstrate scientific methods. Physics I Unit 1 Methods in Science (Systems of Units) Estimated Time Frame Big Ideas for Units 10 Days Tools are needed for the study of Physics, such as measurement, conversions, significant figures,

More information

Curriculum Map-- Kings School District Honors Physics

Curriculum Map-- Kings School District Honors Physics Curriculum Map-- Kings School District Honors Physics Big ideas Essential Questions Content Skills/Standards Assessment + Criteria Activities/Resources Motion of an object can be described by its position,

More information

Physics for Scientists and Engineers 4th Edition, 2017

Physics for Scientists and Engineers 4th Edition, 2017 A Correlation of Physics for Scientists and Engineers 4th Edition, 2017 To the AP Physics C: Mechanics Course Descriptions AP is a trademark registered and/or owned by the College Board, which was not

More information

Course Name: AP Physics. Team Names: Jon Collins. Velocity Acceleration Displacement

Course Name: AP Physics. Team Names: Jon Collins. Velocity Acceleration Displacement Course Name: AP Physics Team Names: Jon Collins 1 st 9 weeks Objectives Vocabulary 1. NEWTONIAN MECHANICS and lab skills: Kinematics (including vectors, vector algebra, components of vectors, coordinate

More information

Chapter 07: Kinetic Energy and Work

Chapter 07: Kinetic Energy and Work Chapter 07: Kinetic Energy and Work Conservation of Energy is one of Nature s fundamental laws that is not violated. Energy can take on different forms in a given system. This chapter we will discuss work

More information

Mass on a Horizontal Spring

Mass on a Horizontal Spring Course- B.Sc. Applied Physical Science (Computer Science) Year- IInd, Sem- IVth Subject Physics Paper- XIVth, Electromagnetic Theory Lecture No. 22, Simple Harmonic Motion Introduction Hello friends in

More information

PSI AP Physics I Work and Energy

PSI AP Physics I Work and Energy PSI AP Physics I Work and Energy Multiple-Choice questions 1. A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to accelerate

More information

Raymond A. Serway Chris Vuille. Chapter Thirteen. Vibrations and Waves

Raymond A. Serway Chris Vuille. Chapter Thirteen. Vibrations and Waves Raymond A. Serway Chris Vuille Chapter Thirteen Vibrations and Waves Periodic Motion and Waves Periodic motion is one of the most important kinds of physical behavior Will include a closer look at Hooke

More information

Energy Problem Solving Techniques.

Energy Problem Solving Techniques. 1 Energy Problem Solving Techniques www.njctl.org 2 Table of Contents Introduction Gravitational Potential Energy Problem Solving GPE, KE and EPE Problem Solving Conservation of Energy Problem Solving

More information

AP PHYSICS 1 Learning Objectives Arranged Topically

AP PHYSICS 1 Learning Objectives Arranged Topically AP PHYSICS 1 Learning Objectives Arranged Topically with o Big Ideas o Enduring Understandings o Essential Knowledges o Learning Objectives o Science Practices o Correlation to Knight Textbook Chapters

More information

REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions

REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions Question 1 (Adapted from DBE November 2014, Question 2) Two blocks of masses 20 kg and 5 kg respectively are connected by a light inextensible string,

More information

NYS STANDARD/KEY IDEA/PERFORMANCE INDICATOR 5.1 a-e. 5.1a Measured quantities can be classified as either vector or scalar.

NYS STANDARD/KEY IDEA/PERFORMANCE INDICATOR 5.1 a-e. 5.1a Measured quantities can be classified as either vector or scalar. INDICATOR 5.1 a-e September Unit 1 Units and Scientific Notation SI System of Units Unit Conversion Scientific Notation Significant Figures Graphical Analysis Unit Kinematics Scalar vs. vector Displacement/dis

More information

Good Vibes: Introduction to Oscillations

Good Vibes: Introduction to Oscillations Good Vibes: Introduction to Oscillations Description: Several conceptual and qualitative questions related to main characteristics of simple harmonic motion: amplitude, displacement, period, frequency,

More information

Curriculum Map-- Kings School District- Physics

Curriculum Map-- Kings School District- Physics Curriculum Map-- Kings School District- Physics Big ideas Essential Questions Content Skills/Standards Assessment + Criteria Activities/Resources Motion of an object can be described by its position, speed,

More information

Recap: Energy Accounting

Recap: Energy Accounting Recap: Energy Accounting Energy accounting enables complex systems to be studied. Total Energy = KE + PE = conserved Even the simple pendulum is not easy to study using Newton s laws of motion, as the

More information

AP Physics C Summer Assignment Kinematics

AP Physics C Summer Assignment Kinematics AP Physics C Summer Assignment Kinematics 1. A car whose speed is 20 m/s passes a stationary motorcycle which immediately gives chase with a constant acceleration of 2.4 m/s 2. a. How far will the motorcycle

More information

September. Text: Physics: Principles & Problems, Merrill-Glencoe NYS STANDARD/KEY IDEA/PERFORMANCE INDICATOR

September. Text: Physics: Principles & Problems, Merrill-Glencoe NYS STANDARD/KEY IDEA/PERFORMANCE INDICATOR September Unit Units and Scientific Notation SI System of Units Unit Conversion Scientific Notation Significant Figures Graphical Analysis Unit Kinematics Scalar vs. vector Displacement/distance Velocity/speed

More information

Quantitative Skills in AP Physics 1

Quantitative Skills in AP Physics 1 This chapter focuses on some of the quantitative skills that are important in your AP Physics 1 course. These are not all of the skills that you will learn, practice, and apply during the year, but these

More information

Practice Problems for Exam 2 Solutions

Practice Problems for Exam 2 Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 008 Practice Problems for Exam Solutions Part I Concept Questions: Circle your answer. 1) A spring-loaded toy dart gun

More information

Circle correct course: PHYS 1P21 or PHYS 1P91 BROCK UNIVERSITY. Course: PHYS 1P21/1P91 Number of students: 260 Examination date: 10 November 2014

Circle correct course: PHYS 1P21 or PHYS 1P91 BROCK UNIVERSITY. Course: PHYS 1P21/1P91 Number of students: 260 Examination date: 10 November 2014 Tutorial #: Circle correct course: PHYS P or PHYS P9 Name: Student #: BROCK UNIVERSITY Test 5: November 04 Number of pages: 5 + formula sheet Course: PHYS P/P9 Number of students: 0 Examination date: 0

More information

AP Physics C - Mechanics

AP Physics C - Mechanics Slide 1 / 84 Slide 2 / 84 P Physics C - Mechanics Energy Problem Solving Techniques 2015-12-03 www.njctl.org Table of Contents Slide 3 / 84 Introduction Gravitational Potential Energy Problem Solving GPE,

More information

the spring is compressed and x is the compression

the spring is compressed and x is the compression Lecture 4 Spring problem and conservation of mechanical energy Hooke's Law The restoring force exerted by the spring is directly proportional to its displacement. The restoring force acts in a direction

More information

Applied Mathematics B Study Guide

Applied Mathematics B Study Guide Science, Engineering and Technology Portfolio School of Life and Physical Sciences Foundation Studies (Applied Science/Engineering) Applied Mathematics B Study Guide Topics Kinematics Dynamics Work, Energy

More information

Periodic Motion. Periodic motion is motion of an object that. regularly repeats

Periodic Motion. Periodic motion is motion of an object that. regularly repeats Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A special kind of periodic motion occurs in mechanical systems

More information

EXPERIMENT 11 The Spring Hooke s Law and Oscillations

EXPERIMENT 11 The Spring Hooke s Law and Oscillations Objectives EXPERIMENT 11 The Spring Hooke s Law and Oscillations To investigate how a spring behaves when it is stretched under the influence of an external force. To verify that this behavior is accurately

More information

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011 PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this

More information

Miami-Dade Community College. PHY 1025 Basic Physics. This course may be used to satisfy one of the Natural Science requirements.

Miami-Dade Community College. PHY 1025 Basic Physics. This course may be used to satisfy one of the Natural Science requirements. Miami-Dade Community College PHY 1025 Basic Physics PHY 1025 3 credits Course Description This course will facilitate the transition from high school to college/university physics. Content includes units

More information

Good Vibes: Introduction to Oscillations

Good Vibes: Introduction to Oscillations Chapter 14 Solutions Good Vibes: Introduction to Oscillations Description: Several conceptual and qualitative questions related to main characteristics of simple harmonic motion: amplitude, displacement,

More information

STEP Support Programme. Mechanics STEP Questions

STEP Support Programme. Mechanics STEP Questions STEP Support Programme Mechanics STEP Questions This is a selection of mainly STEP I questions with a couple of STEP II questions at the end. STEP I and STEP II papers follow the same specification, the

More information

Lab/Demo 5 Periodic Motion and Momentum PHYS 1800

Lab/Demo 5 Periodic Motion and Momentum PHYS 1800 Lab/Demo 5 Periodic Motion and Momentum PHYS 1800 Objectives: Learn to recognize and describe periodic motion. Develop some intuition for the principle of conservation of energy in periodic systems. Use

More information

4 A mass-spring oscillating system undergoes SHM with a period T. What is the period of the system if the amplitude is doubled?

4 A mass-spring oscillating system undergoes SHM with a period T. What is the period of the system if the amplitude is doubled? Slide 1 / 52 1 A block with a mass M is attached to a spring with a spring constant k. The block undergoes SHM. Where is the block located when its velocity is a maximum in magnitude? A 0 B + or - A C

More information

Recall: Gravitational Potential Energy

Recall: Gravitational Potential Energy Welcome back to Physics 15 Today s agenda: Work Power Physics 15 Spring 017 Lecture 10-1 1 Recall: Gravitational Potential Energy For an object of mass m near the surface of the earth: U g = mgh h is height

More information

Chapter 11 Vibrations and Waves

Chapter 11 Vibrations and Waves Chapter 11 Vibrations and Waves If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system

More information

Chapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.

Chapter 14 Oscillations. Copyright 2009 Pearson Education, Inc. Chapter 14 Oscillations 14-1 Oscillations of a Spring If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The

More information

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m

(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m PSI AP Physics C Work and Energy (Algebra Based) Multiple Choice Questions (use g = 10 m/s 2 ) 1. A student throws a ball upwards from the ground level where gravitational potential energy is zero. At

More information

AP Physics C Mechanics

AP Physics C Mechanics 1 AP Physics C Mechanics Simple Harmonic Motion 2015 12 05 www.njctl.org 2 Table of Contents Click on the topic to go to that section Spring and a Block Energy of SHM SHM and UCM Simple and Physical Pendulums

More information

Chap. 15: Simple Harmonic Motion

Chap. 15: Simple Harmonic Motion Chap. 15: Simple Harmonic Motion Announcements: CAPA is due next Tuesday and next Friday. Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/ Examples of periodic motion vibrating guitar

More information

4) Vector = and vector = What is vector = +? A) B) C) D) E)

4) Vector = and vector = What is vector = +? A) B) C) D) E) 1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In

More information

Sometimes (like on AP test) you will see the equation like this:

Sometimes (like on AP test) you will see the equation like this: Work, Energy & Momentum Notes Chapter 5 & 6 The two types of energy we will be working with in this unit are: (K in book KE): Energy associated with of an object. (U in book PE): Energy associated with

More information

AP Physics C: Mechanics Practice (Systems of Particles and Linear Momentum)

AP Physics C: Mechanics Practice (Systems of Particles and Linear Momentum) AP Physics C: Mechanics Practice (Systems of Particles and Linear Momentum) 1980M2. A block of mass m slides at velocity v o across a horizontal frictionless surface toward a large curved movable ramp

More information

Regents Physics. Physics Midterm Review - Multiple Choice Problems

Regents Physics. Physics Midterm Review - Multiple Choice Problems Name Physics Midterm Review - Multiple Choice Problems Regents Physics 1. A car traveling on a straight road at 15.0 meters per second accelerates uniformly to a speed of 21.0 meters per second in 12.0

More information

AHL 9.1 Energy transformation

AHL 9.1 Energy transformation AHL 9.1 Energy transformation 17.1.2018 1. [1 mark] A pendulum oscillating near the surface of the Earth swings with a time period T. What is the time period of the same pendulum near the surface of the

More information

Physics C: Mechanics

Physics C: Mechanics Physics C: Mechanics 2013 2014 PISCATAWAY TOWNSHIP SCHOOLS COURSE SYLLABUS Mr. Rohan Gokhale rgokhale@pway.org www.piscatawayschools.org/phs Brief Description of Course The AP Physics course is a full

More information

Northwestern Connecticut Community College Course Syllabus

Northwestern Connecticut Community College Course Syllabus Northwestern Connecticut Community College Course Syllabus Course Title: Introductory Physics Course #: PHY 110 Course Description: 4 credits (3 class hours and 3 laboratory hours per week) Physics 110

More information

Chapter 14: Periodic motion

Chapter 14: Periodic motion Chapter 14: Periodic motion Describing oscillations Simple harmonic motion Energy of simple harmonic motion Applications of simple harmonic motion Simple pendulum & physical pendulum Damped oscillations

More information

Simple Harmonic Motion Practice Problems PSI AP Physics 1

Simple Harmonic Motion Practice Problems PSI AP Physics 1 Simple Harmonic Motion Practice Problems PSI AP Physics 1 Name Multiple Choice Questions 1. A block with a mass M is attached to a spring with a spring constant k. The block undergoes SHM. Where is the

More information

Physics-MC Page 1 of 29 Inertia, Force and Motion 1.

Physics-MC Page 1 of 29 Inertia, Force and Motion 1. Physics-MC 2006-7 Page 1 of 29 Inertia, Force and Motion 1. 3. 2. Three blocks of equal mass are placed on a smooth horizontal surface as shown in the figure above. A constant force F is applied to block

More information

Chapter 14 Oscillations

Chapter 14 Oscillations Chapter 14 Oscillations If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a

More information

11. (7 points: Choose up to 3 answers) What is the tension,!, in the string? a.! = 0.10 N b.! = 0.21 N c.! = 0.29 N d.! = N e.! = 0.

11. (7 points: Choose up to 3 answers) What is the tension,!, in the string? a.! = 0.10 N b.! = 0.21 N c.! = 0.29 N d.! = N e.! = 0. A harmonic wave propagates horizontally along a taut string of length! = 8.0 m and mass! = 0.23 kg. The vertical displacement of the string along its length is given by!!,! = 0.1!m cos 1.5!!! +!0.8!!,

More information

The content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam.

The content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam. WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system is always

More information

Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that.

Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. NAME: 4. Units of power include which of the following?

More information

St. Joseph s Anglo-Chinese School

St. Joseph s Anglo-Chinese School Time allowed:.5 hours Take g = 0 ms - if necessary. St. Joseph s Anglo-Chinese School 008 009 First Term Examination Form 6 ASL Physics Section A (40%) Answer ALL questions in this section. Write your

More information

Oscillatory Motion and Wave Motion

Oscillatory Motion and Wave Motion Oscillatory Motion and Wave Motion Oscillatory Motion Simple Harmonic Motion Wave Motion Waves Motion of an Object Attached to a Spring The Pendulum Transverse and Longitudinal Waves Sinusoidal Wave Function

More information

Oscillatory Motion SHM

Oscillatory Motion SHM Chapter 15 Oscillatory Motion SHM Dr. Armen Kocharian Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A

More information

AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.

AP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh. 1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach

More information

Wiley Plus. Final Assignment (5) Is Due Today: Before 11 pm!

Wiley Plus. Final Assignment (5) Is Due Today: Before 11 pm! Wiley Plus Final Assignment (5) Is Due Today: Before 11 pm! Final Exam Review December 9, 009 3 What about vector subtraction? Suppose you are given the vector relation A B C RULE: The resultant vector

More information

Newton s Laws of Motion

Newton s Laws of Motion Chapter 4 Newton s Second Law: in vector form Newton s Laws of Motion σ റF = m റa in component form σ F x = ma x σ F y = ma y in equilibrium and static situations a x = 0; a y = 0 Strategy for Solving

More information

https://njctl.org/courses/science/ap-physics-c-mechanics/attachments/summerassignment-3/

https://njctl.org/courses/science/ap-physics-c-mechanics/attachments/summerassignment-3/ AP Physics C Summer Assignment 2017 1. Complete the problem set that is online, entitled, AP C Physics C Summer Assignment 2017. I also gave you a copy of the problem set. You may work in groups as a matter

More information

PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009

PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively.

More information

CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CHAPTER 6 WORK AND ENERGY ANSWERS TO FOCUS ON CONCEPTS QUESTIONS (e) When the force is perpendicular to the displacement, as in C, there is no work When the force points in the same direction as the displacement,

More information

Mechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time.

Mechanics. Time (s) Distance (m) Velocity (m/s) Acceleration (m/s 2 ) = + displacement/time. Mechanics Symbols: Equations: Kinematics The Study of Motion s = distance or displacement v = final speed or velocity u = initial speed or velocity a = average acceleration s u+ v v v u v= also v= a =

More information

Chapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.

Chapter 14 Oscillations. Copyright 2009 Pearson Education, Inc. Chapter 14 Oscillations Oscillations of a Spring Simple Harmonic Motion Energy in the Simple Harmonic Oscillator Simple Harmonic Motion Related to Uniform Circular Motion The Simple Pendulum The Physical

More information

= y(x, t) =A cos (!t + kx)

= y(x, t) =A cos (!t + kx) A harmonic wave propagates horizontally along a taut string of length L = 8.0 m and mass M = 0.23 kg. The vertical displacement of the string along its length is given by y(x, t) = 0. m cos(.5 t + 0.8

More information

Lab 10: Harmonic Motion and the Pendulum

Lab 10: Harmonic Motion and the Pendulum Lab 10 Harmonic Motion and the Pendulum 119 Name Date Partners Lab 10: Harmonic Motion and the Pendulum OVERVIEW A body is said to be in a position of stable equilibrium if, after displacement in any direction,

More information

_CH01_p qxd 1/20/10 8:35 PM Page 1 PURPOSE

_CH01_p qxd 1/20/10 8:35 PM Page 1 PURPOSE 9460218_CH01_p001-010.qxd 1/20/10 8:35 PM Page 1 1 GRAPHING AND ANALYSIS PURPOSE The purpose of this lab is to investigate the relationship between displacement and force in springs and to practice acquiring

More information

Outline. Hook s law. Mass spring system Simple harmonic motion Travelling waves Waves in string Sound waves

Outline. Hook s law. Mass spring system Simple harmonic motion Travelling waves Waves in string Sound waves Outline Hook s law. Mass spring system Simple harmonic motion Travelling waves Waves in string Sound waves Hooke s Law Force is directly proportional to the displacement of the object from the equilibrium

More information

LAB 10: HARMONIC MOTION AND THE PENDULUM

LAB 10: HARMONIC MOTION AND THE PENDULUM 163 Name Date Partners LAB 10: HARMONIC MOION AND HE PENDULUM Galileo reportedly began his study of the pendulum in 1581 while watching this chandelier swing in Pisa, Italy OVERVIEW A body is said to be

More information

PHYSICS. Curriculum Standard One: The student will understand that Newton s laws predict the motion of most objects.

PHYSICS. Curriculum Standard One: The student will understand that Newton s laws predict the motion of most objects. Science Motion and Forces 11-12 Curriculum Standard One: The student will understand that Newton s laws predict the motion of most objects. *1A. The student will demonstrate an problems involving constant

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 Work and Energy Midterm exams will be available next Thursday. Assignment 6 Textbook (Giancoli, 6 th edition), Chapter 6: Due on Thursday, November 5 1. On page 162 of Giancoli, problem 4. 2.

More information

AP Physics C Mechanics Objectives

AP Physics C Mechanics Objectives AP Physics C Mechanics Objectives I. KINEMATICS A. Motion in One Dimension 1. The relationships among position, velocity and acceleration a. Given a graph of position vs. time, identify or sketch a graph

More information

ME 230 Kinematics and Dynamics

ME 230 Kinematics and Dynamics ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Lecture 6: Particle Kinetics Kinetics of a particle (Chapter 13) - 13.4-13.6 Chapter 13: Objectives

More information

Northwestern CT Community College Course Syllabus. Course Title: CALCULUS-BASED PHYSICS I with Lab Course #: PHY 221

Northwestern CT Community College Course Syllabus. Course Title: CALCULUS-BASED PHYSICS I with Lab Course #: PHY 221 Northwestern CT Community College Course Syllabus Course Title: CALCULUS-BASED PHYSICS I with Lab Course #: PHY 221 Course Description: 4 credits (3 class hours and 3 laboratory hours per week) Physics

More information

Chapter 15. Oscillatory Motion

Chapter 15. Oscillatory Motion Chapter 15 Oscillatory Motion Part 2 Oscillations and Mechanical Waves Periodic motion is the repeating motion of an object in which it continues to return to a given position after a fixed time interval.

More information

Honor Physics Final Exam Review. What is the difference between series, parallel, and combination circuits?

Honor Physics Final Exam Review. What is the difference between series, parallel, and combination circuits? Name Period Date Honor Physics Final Exam Review Circuits You should be able to: Calculate the total (net) resistance of a circuit. Calculate current in individual resistors and the total circuit current.

More information

Chapter 14. Oscillations. Oscillations Introductory Terminology Simple Harmonic Motion:

Chapter 14. Oscillations. Oscillations Introductory Terminology Simple Harmonic Motion: Chapter 14 Oscillations Oscillations Introductory Terminology Simple Harmonic Motion: Kinematics Energy Examples of Simple Harmonic Oscillators Damped and Forced Oscillations. Resonance. Periodic Motion

More information

AHL 9.1 Energy transformation

AHL 9.1 Energy transformation AHL 9.1 Energy transformation 17.1.2018 1. [1 mark] A pendulum oscillating near the surface of the Earth swings with a time period T. What is the time period of the same pendulum near the surface of the

More information

α f k θ y N m mg Figure 1 Solution 1: (a) From Newton s 2 nd law: From (1), (2), and (3) Free-body diagram (b) 0 tan 0 then

α f k θ y N m mg Figure 1 Solution 1: (a) From Newton s 2 nd law: From (1), (2), and (3) Free-body diagram (b) 0 tan 0 then Question [ Work ]: A constant force, F, is applied to a block of mass m on an inclined plane as shown in Figure. The block is moved with a constant velocity by a distance s. The coefficient of kinetic

More information

Physics 5A Final Review Solutions

Physics 5A Final Review Solutions Physics A Final Review Solutions Eric Reichwein Department of Physics University of California, Santa Cruz November 6, 0. A stone is dropped into the water from a tower 44.m above the ground. Another stone

More information

Physics 1C. Lecture 12B

Physics 1C. Lecture 12B Physics 1C Lecture 12B SHM: Mathematical Model! Equations of motion for SHM:! Remember, simple harmonic motion is not uniformly accelerated motion SHM: Mathematical Model! The maximum values of velocity

More information

Wheel and Axle. Author: Joseph Harrison. Research Ans Aerospace Engineering 1 Expert, Monash University

Wheel and Axle. Author: Joseph Harrison. Research Ans Aerospace Engineering 1 Expert, Monash University Wheel and Axle Author: Joseph Harrison British Middle-East Center for studies & Research info@bmcsr.com http:// bmcsr.com Research Ans Aerospace Engineering 1 Expert, Monash University Introduction A solid

More information

Exam #2, Chapters 5-7 PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam #2, Chapters 5-7 PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam #2, Chapters 5-7 Name PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The quantity 1/2 mv2 is A) the potential energy of the object.

More information

W = F Δx or W = F Δx cosθ

W = F Δx or W = F Δx cosθ WORK AND ENERGY When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. In order for a force to qualify as having done work on an object,

More information

Physics 12. Unit 5 Circular Motion and Gravitation Part 1

Physics 12. Unit 5 Circular Motion and Gravitation Part 1 Physics 12 Unit 5 Circular Motion and Gravitation Part 1 1. Nonlinear motions According to the Newton s first law, an object remains its tendency of motion as long as there is no external force acting

More information

Potential Energy & Conservation of Energy

Potential Energy & Conservation of Energy PHYS 101 Previous Exam Problems CHAPTER 8 Potential Energy & Conservation of Energy Potential energy Conservation of energy conservative forces Conservation of energy friction Conservation of energy external

More information

AP Physics C - Mechanics

AP Physics C - Mechanics Slide 1 / 125 Slide 2 / 125 AP Physics C - Mechanics Work and Energy 2015-12-03 www.njctl.org Table of Contents Slide 3 / 125 Click on the topic to go to that section Energy and Work Conservative and Non-Conservative

More information

AP Mechanics Summer Assignment

AP Mechanics Summer Assignment 2012-2013 AP Mechanics Summer Assignment To be completed in summer Submit for grade in September Name: Date: Equations: Kinematics (For #1 and #2 questions: use following equations only. Need to show derivation

More information

Chapter 9 Linear Momentum and Collisions

Chapter 9 Linear Momentum and Collisions Chapter 9 Linear Momentum and Collisions The Center of Mass The center of mass of a system of particles is the point that moves as though (1) all of the system s mass were concentrated there and (2) all

More information

CHAPTER 7: OSCILLATORY MOTION REQUIRES A SET OF CONDITIONS

CHAPTER 7: OSCILLATORY MOTION REQUIRES A SET OF CONDITIONS CHAPTER 7: OSCILLATORY MOTION REQUIRES A SET OF CONDITIONS 7.1 Period and Frequency Anything that vibrates or repeats its motion regularly is said to have oscillatory motion (sometimes called harmonic

More information

AP Physics C 2015 Summer Assignment

AP Physics C 2015 Summer Assignment AP Physics C 2015 Summer Assignment College Board (the people in charge of AP exams) recommends students to only take AP Physics C if they have already taken a 1 st year physics course and are currently

More information

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for AP Physics, Mechanics C

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for AP Physics, Mechanics C Curriculum Map for AP Physics, Mechanics C September Enduring Understandings (The big ideas): Chapter 2 -- Motion Along a Straight Line Essential Questions: How do objects move? 1. Displacement, time,

More information

PHYSICS 1. Section I 40 Questions Time 90 minutes. g = 10 m s in all problems.

PHYSICS 1. Section I 40 Questions Time 90 minutes. g = 10 m s in all problems. Note: To simplify calculations, you may use PHYSICS 1 Section I 40 Questions Time 90 minutes 2 g = 10 m s in all problems. Directions: Each of the questions or incomplete statements below is followed by

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 11-1: SIMPLE HARMONIC MOTION LSN 11-: ENERGY IN THE SIMPLE HARMONIC OSCILLATOR LSN 11-3: PERIOD AND THE SINUSOIDAL NATURE OF SHM Introductory Video:

More information

Tentative Physics 1 Standards

Tentative Physics 1 Standards Tentative Physics 1 Standards Mathematics MC1. Arithmetic: I can add, subtract, multiply, and divide real numbers, take their natural and common logarithms, and raise them to real powers and take real

More information

Broward County Schools AP Physics 1 Review

Broward County Schools AP Physics 1 Review Broward County Schools AP Physics 1 Review 1 AP Physics 1 Review 1. The Basics of the Exam Important info: No penalty for guessing. Eliminate one or two choices and then take a shot. Multi-select questions

More information

7-6 Inelastic Collisions

7-6 Inelastic Collisions 7-6 Inelastic Collisions With inelastic collisions, some of the initial kinetic energy is lost to thermal or potential energy. It may also be gained during explosions, as there is the addition of chemical

More information

Chapter 5: Energy. Energy is one of the most important concepts in the world of science. Common forms of Energy

Chapter 5: Energy. Energy is one of the most important concepts in the world of science. Common forms of Energy Chapter 5: Energy Energy is one of the most important concepts in the world of science. Common forms of Energy Mechanical Chemical Thermal Electromagnetic Nuclear One form of energy can be converted to

More information

Corso di Laurea in LOGOPEDIA FISICA ACUSTICA MOTO OSCILLATORIO

Corso di Laurea in LOGOPEDIA FISICA ACUSTICA MOTO OSCILLATORIO Corso di Laurea in LOGOPEDIA FISICA ACUSTICA MOTO OSCILLATORIO Fabio Romanelli Department of Mathematics & Geosciences University of Trieste Email: romanel@units.it What is an Oscillation? Oscillation

More information

Conservation of Linear Momentum

Conservation of Linear Momentum Conservation of Linear Momentum Objective In this series of experiments, the conservation of linear momentum and kinetic energy will be tested for different types of collisions. Equipment List Air track,

More information